Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Need solution ! [#permalink]
04 Aug 2010, 21:46

6

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

nusmavrik wrote:

If x and y are positive integers, what is the remainder when x is divided by y? (1) When x is divided by 2y, the remainder is 4 (2) When x + y is divided by y, the remainder is 4

Positive integer x divided by positive integer y yields remainder of r can be expressed as x=yq+r. Question is r=?

(1) When x is divided by 2y, the remainder is 4. If x=20 and y=8 (satisfies the given statemnet as 20 divided by 2*8=16 yields reminder of 4), then x divided by y yields r=4 (20 divided by 8 yields remainder of 4) BUT if x=10 and y=3 (satisfies the given statemnet as 10 divided by 2*3=6 yields reminder of 4), then x divided by y yields r=1 (10 divided by 3 yields remainder of 1). Two different answers. Not sufficient.

(2) When x + y is divided by y, the remainder is 4 --> x+y=yp+4 --> x=y(p-1)+4 (x is 4 more than multiple of y)--> this statement directly tells us that x divided by y yields remainder of 4. Sufficient.

Re: If x and y are positive integers, what is the remainder when [#permalink]
16 Nov 2011, 21:50

6

This post received KUDOS

Expert's post

nusmavrik wrote:

If x and y are positive integers, what is the remainder when x is divided by y? (1) When x is divided by 2y, the remainder is 4 (2) When x + y is divided by y, the remainder is 4

Stmnt 1: When x is divided by 2y, the remainder is 4

When you divide x by 2y, you make groups with 2y balls in each and you have 4 balls leftover. Instead, if you divide x by y, you may have 4 balls leftover or you may have fewer balls if y is less than or equal to 4 i.e. say if y = 3, you could make another group of 3 balls and you will have only 1 ball leftover. So you could have different remainders. Not sufficient.

Stmnt 2: When x + y is divided by y, the remainder is 4

When you make groups of y balls each from (x+y), the y balls make 1 group and you are left with x balls. If the remainder is 4, it means when you make groups of y balls each from x balls, you have 4 balls leftover. Since the question asks us: how many balls are leftover when you make groups of y balls from x balls, you get your answer directly as '4'. Sufficient.

Re: Need solution ! [#permalink]
11 Nov 2011, 20:24

1

This post received KUDOS

Bunuel wrote:

That's a good question. A. x=y(2k)+4, k any integer >=0. B. x=y(p-1)+4, p any integer >=0.

Why A is not sufficient to determine the remainder and B is? Why did I use number plugging to show this in the first case and didn't in the second?

If we are told that x divided by y gives a remainder of 4, means x=yp+4 where p is integer >=0. We don't know x and y so p (quotient) can be any integer.

Look at equation A, the quotient is 2k, 2k is even. It can be rephrased as x divided by y will give the remainder of 4 IF quotient is even. But what about the cases when quotient is odd? We don't know that so we must check to determine this.

As for B. Quotient here is (p-1), which for integer values of p can give us ANY value: any even as well as any odd. So basically x=y(p-1)+4 is the same as x=yp+4. No need for double checking.

Hope it's clear.

Bunuel could we say the following? (Having in mind that the Remainder depends on the divisor)

(1) When x is divided by 2y, the remainder is 4

statement 1 ----> x=2*y*k+4, k integer

Therefore because the divisor has to be larger (not equal because it is stated that a reminder exists) than the remainder: 2*y>4 --> y>2 -->y>=3

If y (divisor) is smaller than 4 then the remainder changes and if it is larger than 4 the remainder is 4.

For example: if y=3 then x=2*3*k+3+1, R=1 if y=4 then x=4*2*k+4+0, R=0 (if y=5 then x=2*5k+4, R=4)

Therefore Insufficient.

2) When x + y is divided by y, the remainder is 4

statement 2 ----> x+y=y*k+4, k integer

We are told that the remainder is 4, therefore y>=5! Which means that remainder will always be 4.

Re: Need solution ! [#permalink]
24 Feb 2011, 11:30

Bunuel wrote:

nusmavrik wrote:

If x and y are positive integers, what is the remainder when x is divided by y? (1) When x is divided by 2y, the remainder is 4 (2) When x + y is divided by y, the remainder is 4

Positive integer x divided by positive integer y yields remainder of r can be expressed as x=yq+r. Question is r=?

(1) When x is divided by 2y, the remainder is 4. If x=20 and y=8 (satisfies the given statemnet as 20 divided by 2*8=16 yields reminder of 4), then x divided by y yields r=4 (20 divided by 8 yields remainder of 4) BUT if x=10 and y=3 (satisfies the given statemnet as 10 divided by 2*3=6 yields reminder of 4), then x divided by y yields r=1 (10 divided by 3 yields remainder of 1). Two different answers. Not sufficient.

(2) When x + y is divided by y, the remainder is 4 --> x+y=yp+4 --> x=y(p-1)+4 (x is 4 more than multiple of y)--> this statement directly tells us that x divided by y yields remainder of 4. Sufficient.

Answer: B.

Hope it's clear.

I'm confused. With the same proof given for the second point, could I not convince myself that 1 would suffice? eg: x = yp + r From (1) I could say x = 2yp + 4 (or) x = (2p)y + 4 Clearly this statement tells us that x is 4 more than a multiple of y as well. Why can I not convince myself at this step that the statement would suffice? Although, the statement does not suffice since the logic fails when you plug in (x=10,y=3) .

Re: Need solution ! [#permalink]
24 Feb 2011, 11:40

Expert's post

bugSniper wrote:

Bunuel wrote:

nusmavrik wrote:

If x and y are positive integers, what is the remainder when x is divided by y? (1) When x is divided by 2y, the remainder is 4 (2) When x + y is divided by y, the remainder is 4

Positive integer x divided by positive integer y yields remainder of r can be expressed as x=yq+r. Question is r=?

(1) When x is divided by 2y, the remainder is 4. If x=20 and y=8 (satisfies the given statemnet as 20 divided by 2*8=16 yields reminder of 4), then x divided by y yields r=4 (20 divided by 8 yields remainder of 4) BUT if x=10 and y=3 (satisfies the given statemnet as 10 divided by 2*3=6 yields reminder of 4), then x divided by y yields r=1 (10 divided by 3 yields remainder of 1). Two different answers. Not sufficient.

(2) When x + y is divided by y, the remainder is 4 --> x+y=yp+4 --> x=y(p-1)+4 (x is 4 more than multiple of y)--> this statement directly tells us that x divided by y yields remainder of 4. Sufficient.

Answer: B.

Hope it's clear.

I'm confused. With the same proof given for the second point, could I not convince myself that 1 would suffice? eg: x = yp + r From (1) I could say x = 2yp + 4 (or) x = (2p)y + 4 Clearly this statement tells us that x is 4 more than a multiple of y as well. Why can I not convince myself at this step that the statement would suffice? Although, the statement does not suffice since the logic fails when you plug in (x=10,y=3) .

That's a good question. A. x=y(2k)+4, k any integer >=0. B. x=y(p-1)+4, p any integer >=0.

Why A is not sufficient to determine the remainder and B is? Why did I use number plugging to show this in the first case and didn't in the second?

If we are told that x divided by y gives a remainder of 4, means x=yp+4 where p is integer >=0. We don't know x and y so p (quotient) can be any integer.

Look at equation A, the quotient is 2k, 2k is even. It can be rephrased as x divided by y will give the remainder of 4 IF quotient is even. But what about the cases when quotient is odd? We don't know that so we must check to determine this.

As for B. Quotient here is (p-1), which for integer values of p can give us ANY value: any even as well as any odd. So basically x=y(p-1)+4 is the same as x=yp+4. No need for double checking.

Re: Need solution ! [#permalink]
24 Feb 2011, 11:53

B is sufficient by using the rule of remainders additive property: (x+y)/y leaves a remainder of 4. Means: remainder left by x/y + remainder left by y/y = 4 remainder left by x/y+0=4 remainder left by x/y=4

Re: If x and y are positive integers, what is the remainder when [#permalink]
17 Nov 2011, 08:23

Karishma...Really impressive reply..!! Very precise..and easily understandable...went through your post too...had never imagined division from this perspective...i think this is a better approach to these questions..! Thanks for sharing! _________________

Re: If x and y are positive integers, what is the remainder when [#permalink]
17 Nov 2011, 08:58

I must admit,initially,i did get trapped in option A & B both and would've answered both are sufficient,but carefully after evaluating,realized, only B suffices. A doesn't.

Re: If x and y are positive integers, what is the remainder when [#permalink]
17 Dec 2011, 18:53

Yes a tricky question. Karishma, thank you for the detailed explanation. The concept of "grouping" applied to division, although new to me, is easily understandable and very simple indeed. _________________

Re: Need solution ! [#permalink]
12 Sep 2012, 05:40

Bunuel wrote:

nusmavrik wrote:

If x and y are positive integers, what is the remainder when x is divided by y? (1) When x is divided by 2y, the remainder is 4 (2) When x + y is divided by y, the remainder is 4

Positive integer x divided by positive integer y yields remainder of r can be expressed as x=yq+r. Question is r=?

(1) When x is divided by 2y, the remainder is 4. If x=20 and y=8 (satisfies the given statemnet as 20 divided by 2*8=16 yields reminder of 4), then x divided by y yields r=4 (20 divided by 8 yields remainder of 4) BUT if x=10 and y=3 (satisfies the given statemnet as 10 divided by 2*3=6 yields reminder of 4), then x divided by y yields r=1 (10 divided by 3 yields remainder of 1). Two different answers. Not sufficient.

(2) When x + y is divided by y, the remainder is 4 --> x+y=yp+4 --> x=y(p-1)+4 (x is 4 more than multiple of y)--> this statement directly tells us that x divided by y yields remainder of 4. Sufficient.

Answer: B.

Hope it's clear.

Hi Bunuel,

This time i didn't get the explanation. Can you kindly solve the question using algebraic method rather than using any numbers?

Waiting for clarification. _________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: If x and y are positive integers, what is the remainder when [#permalink]
14 Oct 2013, 01:05

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: If x and y are positive integers, what is the remainder when [#permalink]
03 Mar 2015, 01:17

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Well, I’ve had a busy month! In February I traveled to interview and visit three MBA programs. Earlier in the month I also went to Florida on vacation. This...

One of the reasons why I even considered Tepper is the location. Last summer I stopped in Pittsburgh on the way home from a road trip. We were vacationing...

“Which French bank was fined $613bn for manipulating the Euribor rate?” asked quizmaster Andrew Hill in this year’s FT MBA Quiz. “Société Générale” responded the...

The most time-consuming part of writing the essays comes before and after the act of writing. Jotting down an answer to the questions should take a few hours at most. By then you...